lens help for a new dslr buyer

First, I apologize for what is prob the 100th thread over the years like this (and I did have a post and discussion in beginners forum to decide on a camera). But I have read many of them and am just looking for some current, personal advice as I get ready to make a HUGE investment in a camera (at least for me).

I have only owned point and shoot cameras in the past. I have a 4 year old daughter and want a camera that will focus faster and take sharper images (at normal and longer focal lengths). Will use for daughter at soccer, family trips to the zoo, park, different cities as well as indoors for holidays and special events. I mostly view images on my 27" monitor and occasionally would like to make large prints.

I do take videos and currently own and love the videos on my HX9V (will keep that), but will take casual family video on the dslr as well.

... even kind of considering an 18-250ish superzoom and a 35mm fast prime, but think that is prob not a good idea.

Due to my financial situation (and wife), this will be a one time purchase and the next time I will be able to round up 400ish bucks for a lens will be in 2+ years. My budget is actually about $1500, but will stretch it to get something I am happy with.

What do you guys think about these options? Would you recommend a different lens? Is a flash needed/worth that kind of money over the on camera flash?